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Mathematics
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user170231
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32
Does $\int_{-1}^1\frac{\arctan x}{\text{arctanh}\,x}\,\mathrm{d}x$ have a closed form?
Jun 2, 2015
17
Using complex analysis, show that $\int_0^\infty\frac{\arctan(x)}{1+x^2}\,dx=\frac{\pi^2}8$
Oct 25, 2022
17
Why doesn't using the approximation $\sin x\approx x$ near $0$ work for computing this limit?
Jun 25, 2015
14
What is an intuitive approach to solving $\lim_{n\rightarrow\infty}\biggl(\frac{1}{n^2} + \frac{2}{n^2} + \frac{3}{n^2}+\dots+\frac{n}{n^2}\biggr)$?
Jul 27, 2017
12
Using complex analysis, prove $\int\limits_0^\infty \frac{\log(x) \arctan(x)}{1 + x^2} \, dx = \frac78 \zeta(3)$
Nov 27, 2022
12
How to evaluate $\int \frac{1+x}{1+\sqrt x} dx$
Aug 15, 2016
10
Are there certain conditions that $a_n$ must meet in order for this series to converge?
Sep 25, 2015
10
Find the value of the integral: $\int_{0}^{1}\frac{x}{1+x^4}\arctan(x)\,\mathrm{d}x$
Nov 1, 2023
9
Integrate $\ln^3(\sin(x))$ using Fourier series
Jul 14, 2022
9
Why does this double infinite sum $\sum_{n=1}^\infty \sum_{k=n}^\infty\frac{1}{k!}$ converge to $e$?
Jan 13, 2016
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16
How can I generate an interrupted projection of a world map?
14
Did any storylines or content from The Clone Wars exist prior to its broadcasting?
12
Removing all values from a list that satisfy a given condition
9
MovingAverage to include the average of the first and last elements in a list
8
Joining all the keys of a list of rules that point to matching values